Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156732 | Stochastic Processes and their Applications | 2012 | 21 Pages |
Abstract
We construct fractional Brownian motion, sub-fractional Brownian motion and negative sub-fractional Brownian motion by means of limiting procedures applied to some particle systems. These processes are obtained for full ranges of Hurst parameter.We employ the so-called white noise approach. Our construction is quite general, permitting to obtain also some other Gaussian processes, as well as multidimensional random fields. In particular, we generalize and presumably simplify some results by Hambly and Jones (2007). We also obtain a new class of S′S′-valued density processes, containing as a particular case the density process of Martin-Löf (1976).
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Tomasz Bojdecki, Anna Talarczyk,